Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
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TL;DR: In this article, the authors presented finite-difference solution and analytical solution of the finitedifference approximations based on the standard explicit method to the one-dimensional Burgers equation which arises frequently in the mathematical modelling used to solve problems in fluid dynamics.
232 citations
TL;DR: A fully three-dimensional code has been written to compute the motion of a towed cable based on a robust and stable finite difference approximation to the differential equations derived from basic dynamics.
231 citations
TL;DR: In this paper, Harten et al. presented high-resolution finite difference schemes for solving the nonlinear model Boltzmann equations for the computations of rarefied gas flows.
230 citations
TL;DR: In this paper, an approach based on Pade approximants provides a convenient, accurate reformulation of general anelastic laws in differential form, and the resulting differential operators form a uniformly convergent sequence of increasing order in the time derivative, and all are shown to be causal, stable and dissipation.
Abstract: Summary. Realistic anelastic attenuation laws are usually formulated as convolution operators, but this representation is intractable for time-domain synthetic seismogram methods such as the finite difference method. An approach based on Pade approximants provides a convenient, accurate reformulation of general anelastic laws in differential form. The resulting differential operators form a uniformly convergent sequence of increasing order in the time derivative, and all are shown to be causal, stable and dissi- pative. In the special case of frequency-independent Q, all required coefficients for the operators are obtained in closed form in terms of Legendre polynomials.
Low-order approximants are surprisingly accurate. Finite-difference impulse responses for a plane wave in a constant-Q medium, calculated with the fifth-order convergent, are virtually indistinguishable from the exact solution. The formulation is easily generalized to non-scalar waves. Moreover, this method provides a framework for incorporating amplitude-dependent attenuation into numerical simulations.
230 citations
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17 Dec 2013
TL;DR: In this paper, the authors present the foundations of mimetic finite difference method, inner products and reconstruction operators, as well as the diffusion problem in mixed form and in primal form.
Abstract: 1 Model elliptic problems.- 2 Foundations of mimetic finite difference method.- 3 Mimetic inner products and reconstruction operators.- 4 Mimetic discretization of bilinear forms.- 5 The diffusion problem in mixed form.- 6 The diffusion problem in primal form.- 7 Maxwells equations. 8. The Stokes problem. 9 Elasticity and plates.- 10 Other linear and nonlinear mimetic schemes.- 11 Analysis of parameters and maximum principles.- 12 Diffusion problem on generalized polyhedral meshes.
229 citations